Computing a Minimum Enclosing Strip

This section describes a function to compute a minimal enclosing strip (not necessarily axis-parallel) of a given convex point set. Note that this strip is not unique in general. A strip is the closed region bounded by two parallel lines in the plane.

#include <CGAL/minimum_enclosing_quadrilateral_2.h>

template < class ForwardIterator, class OutputIterator, class Traits >
OutputIterator	minimum_enclosing_strip_2 ( ForwardIterator points_begin, ForwardIterator points_end, OutputIterator o, Traits& t = Default_traits)

computes a minimum enclosing strip of the point set described by [points_begin, points_end), writes its bounding lines to o and returns the past-the-end iterator of this sequence.
If the input range is empty or consists of one element only, o remains unchanged.

Precondition

1. If Traits is specified, it satisfies the requirements stated in section and the value type VT of InputIterator is Traits::Point_2. Otherwise VT is CGAL::Point_2<R> for some representation class R.
2. OutputIterator accepts VT as value type.
3. The points denoted by the range [points_begin, points_end) form the boundary of a convex polygon $$P in counterclockwise orientation.

Implementation

Example

#include <CGAL/Cartesian.h>
#include <CGAL/Point_2.h>
#include <CGAL/Polygon_2.h>
#include <CGAL/point_generators_2.h>
#include <CGAL/random_convex_set_2.h>
#include <CGAL/minimum_enclosing_quadrilateral_2.h>
#include <vector>
#include <iostream>

using CGAL::Random_points_in_square_2;
using CGAL::random_convex_set_2;
using CGAL::minimum_enclosing_strip_2;
using std::back_inserter;
using std::cout;
using std::endl;

typedef CGAL::Cartesian< double >                      R;
typedef R::Point_2                                     Point_2;
typedef R::Line_2                                      Line_2;
typedef CGAL::Polygon_traits_2< R >                    P_traits;
typedef std::vector< Point_2 >                         Cont;
typedef CGAL::Polygon_2< P_traits, Cont >              Polygon_2;
typedef CGAL::Creator_uniform_2< double, Point_2 >     Creator;
typedef Random_points_in_square_2< Point_2, Creator >  Point_generator;

int main()
{
  // build a random convex 20-gon p
  Polygon_2 p;
  random_convex_set_2(20, back_inserter(p), Point_generator(1.0));
  cout << p << endl;

  // compute the minimal enclosing strip p_m of p
  Line_2 p_m[2];
  minimum_enclosing_strip_2(
    p.vertices_begin(), p.vertices_end(), p_m);
  cout << p_m[0] << "\n" << p_m[1] << endl;

  return 0;
}